LR15 — 3D Figure Rotation and Spatial Orientation

🧠 AFCAT Reasoning · LR15 ✈️ AFCAT Level

📌 AFCAT Pattern (LR15): 3D Figure Rotation and Spatial Orientation contributes 2–4 questions per paper. These test your ability to mentally rotate 3D objects and determine how they look from different angles. Cube/dice problems are the most common: opposite faces, visible faces when rotated, and open dice folding.

1. Dice / Cube Problems

Dice Fundamentals

A standard die has 6 faces. Opposite faces always sum to 7: (1,6), (2,5), (3,4)
In AFCAT: the die is NOT standard — faces are defined by the question
Rule: when two positions of the same die are shown, find which faces are opposite
Common faces (visible in both positions) tell you the orientation

Finding Opposite Faces — Method

Two dice positions shown. One face is common/visible in both
Rotate mentally: if face A is on top in position 1 and face B is on top in position 2
The face NOT seen in either position when combined is opposite to a specific face
Use elimination: 3 pairs of opposite faces in a cube (front-back, left-right, top-bottom)

Worked Example — Opposite Faces

Dice shown in Position 1: Top=1, Front=2, Right=3. Position 2: Top=2, Front=4, Right=5.
From Position 1: 1 is opposite to Bottom (face unseen opposite top). When top=1, bottom=6 (if standard). But custom dice: face visible = 1,2,3. The three faces 4,5,6 are the opposite ones respectively.
Approach: faces visible in position 1: 1,2,3 (top,front,right) + their opposites: 6(bottom),5(back),4(left). So: 1 opp 6; 2 opp 5; 3 opp 4. Position 2 (top=2,front=4,right=5): 2 opp 5 ✓; front 4 opp back=3 ✓; right 5 opp left=2 ✓. Confirmed: 1-6, 2-5, 3-4 are opposite pairs.

2. Open Die / Cube Folding

An unfolded (net) cube is shown. You must determine which faces are opposite when folded. Standard cross-pattern: the centre face is opposite to the top face in the cross layout.

Net Folding Rule

In a standard cross-shaped die net (plus sign shape):
The face directly across from another in the same row = they are NOT opposite (they are adjacent).
Faces that are 3 apart in the cross are opposite. For a T-shaped net: visualise folding each flap up.
AFCAT always provides the net — fold each face mentally and identify what ends up on opposite sides.

3. 3D Rotation — Front/Top/Side Views

View Types

Front view: What you see looking straight at the object from the front
Top view (Plan view): Looking down from directly above
Side view: Looking from the left or right
A solid cube block: all views = square. An L-shaped block: views differ by direction

Cube Stacks — Counting

Count visible cubes first from front view
Top view shows the footprint (base area)
Side view confirms depth
Hidden cubes: count from perspective — visible + hidden to maintain structure

📝 AFCAT PYQ3D Figure Rotation — AFCAT Pattern

Q1. A cube has: Top=Red, Front=Blue, Right=Green. After rotating 90° to the right (clockwise when viewed from top), which face is now on Top? (AFCAT I 2025)

(a) Red
(b) Blue
(c) Green
(d) Bottom

Answer: (a) Red
Rotating 90° to the right (clockwise when viewed from above) = rotating around the vertical axis. The top face does NOT change when rotating around a vertical axis — only the front/back/left/right faces cycle. Red (top) stays on top. New arrangement: Original Front(Blue) → becomes Right; Original Right(Green) → becomes Back. Top remains Red.

Q2. In an open die net, faces are labeled 1-6. Face 1 is at top, face 6 at bottom, face 2 adjacent to top on the left of the cross. Face 2 is opposite to: (AFCAT II 2024)

(a) Face 5
(b) Face 4
(c) Face 3
(d) Face 6

Answer: (a) Face 5
In the cross net: the face directly opposite is the one 3 steps away in the folding sequence. Face 2 (left of top in cross) folds to the left side of the cube. Its opposite = the right side. Tracing the net: face 5 would fold to the right side. Therefore face 2 is opposite face 5. Always physically fold or trace with a finger when doing net problems.

Q3. How many cubes are in an arrangement shown as: Front view = 3 wide, 2 tall; Top view = 3 wide, 2 deep? (AFCAT I 2024)

(a) 12
(b) 8
(c) 6
(d) 10

Answer: (a) 12
If front view = 3 wide × 2 tall and top view = 3 wide × 2 deep: the structure is a solid rectangular block of 3 × 2 × 2 = 12 cubes. Width=3, Height=2, Depth=2. Total = 3×2×2=12. This assumes a solid block (no hidden gaps). If some cubes are missing, count from the specific view pattern shown.

⚡ Quick Reference — LR15

Dice Rules

Standard die: opposite faces sum to 7
AFCAT dice: custom — find pairs from positions
Vertical axis rotation: top/bottom unchanged
Horizontal axis rotation: front/back unchanged

Net Folding

Draw and fold mentally step by step
Face at top of cross = opposite to extension below
Adjacent faces in net = adjacent (not opposite) in cube
3 opposite pairs: identify which 6 faces pair up

3D Views

Front view: width × height
Top view: width × depth
Side view: depth × height
Total cubes = W × H × D (solid block)

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